Australian Mathematical Society (AustMS): E-Journals
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The Diophantine equation in quadratic number fields
No full texthttp://dx.doi.org/10.1017/S000497271200033
The general position number of the Cartesian product of two trees
No full texthttp://dx.doi.org/10.1017/S000497271200033
Schr\"{o}dinger operators and the Kato square root problem
No full texthttp://dx.doi.org/10.1017/S000497271200033
Algorithm to construct integro splines
No full textWe study some properties of integro splines. Using these properties, we design an algorithm to construct splines of neighbouring degrees to the given spline with degree . A local integro-sextic spline is constructed with the proposed algorithm. The local integro splines work efficiently, that is, they have low computational complexity, and they are effective for use in real time. The construction of nonlocal integro splines usually leads to solving a system of linear equations with band matrices, which yields high computational costs.
doi:10.1017/S144618112100031
On a weighted sum of multiple -values of fixed weight and depth
No full texthttp://dx.doi.org/10.1017/S000497271200033
Being Cayley automatic is closed under taking wreath product with virtually cyclic groups
No full texthttp://dx.doi.org/10.1017/S000497271200033
Estimates for approximate solutions to a functional differential equation model of cell division
No full textThe functional partial differential equation (FPDE) for cell division,
is not amenable to analytical solution techniques, despite being closely related to the first order partial differential equation (PDE)
which, with known , can be solved by the method of characteristics. The difficulty is due to the advanced functional terms and , where , which arise because cells of size are created when cells of size and divide.
The nonnegative function, , denotes the density of cells at time with respect to cell size . The functions , and are, respectively, the growth rate, splitting rate and death rate of cells of size . The total number of cells, , coincides with the norm of . The goal of this paper is to find estimates in (and, with some restrictions, for p>1) for a sequence of approximate solutions to the FPDE that are generated by solving the first order PDE. Our goal is to provide a framework for the analysis and computation of such FPDEs, and we give examples of such computations at the end of the paper.
doi:10.1017/S144618112100005
Points of small height on affine varieties defined over function fields of finite transcendence degree
No full texthttp://dx.doi.org/10.1017/S000497271200033
Integral means of univalent functions on an annulus
No full texthttp://dx.doi.org/10.1017/S000497271200033
Estimates and rigidity for stable solutions to some nonlinear elliptic problems
No full textThe thesis deals with the study of elliptic Partial Differential Equations. It is divided into two parts, the first one concerning a nonlinear elliptic equation involving the p-Laplacian, and the second one focused on a nonlocal problem arising from a model for water waves